where \(\hat{P}_{\bf p}^{(\pm )}=\left[ 1\pm (\hat{\mbox{$\sigma $}}\cdot {\bf p})/p\right] /2\)  are the projection operators on the conduction (\(+\) ) and valence
(\(-\) ) bands, \(\hat{\mbox{$\sigma $}}\)  is the isospin Pauli matrix, and
\(g=(\bar{V}^2 l_c/\hbar \upsilon )^2\pi /2\)  is the coupling constant.
Here we restrict ourselves by the Born approximation when the self-energy
contribution \(\varepsilon (\Lambda _\varepsilon +ig)\)  is written through the logarithmically-divergent real correction and the damping factor.
Note, that these corrections vanish at \(\varepsilon \rightarrow 0\) . From
a comparision with the mobility data [1]}, [2]} one obtains that the parameters \(g\simeq \) 0.45, 0.3, and 0.15 correspond to the sheet resistances \(\sim \) 6, \(\sim \) 4, and \(\sim \) 2 k\(\Omega \)  per square, respectively. The density of states, \(\rho _\varepsilon =-4{\rm Im}\sum _{\bf p}{\rm tr}\hat{G}_{\varepsilon ,{\bf p}}^R\)  is shown in Fig. 2a and \(\rho _\varepsilon =\rho _{-\varepsilon }\) , i. e. the electron-hole symmetry is not violate
due to disorder. Since \(\rho _\varepsilon \)  increases in comparision to the ideal case, \(\overline{\rho }_\varepsilon =2|\varepsilon |/[(\hbar \upsilon )^2\pi ]\) , the energy-dependent renormalized velocity, \(\upsilon V_\varepsilon \) 
decreases up to 10% if \(g\le \) 0.5 and the concentration of carriers in
an intrinsic graphene increases up to 2 times, see Figs. 2b and 2c, respectively (here \(n_T\simeq 8.1\times 10^{10}\)  cm\(^{-2}\)  is the equilibrium
concentration at room temperature and at \(g\rightarrow \) 0).
<FIGURE><FIGURE>